Parallel lines run in the same direction without ever touching. You might think of parallel episodes in a text as running along the same lines without necessarily touching. They're episodes of the play that seem designed to comment on each other, contrast with each other, or in some way to communicate.
For a good example, have a look at Shakespeare's "Julius Caesar". Act III, Scene III has Cinna the poet murdered on the streets by thugs simply because of his name. Act III, IV has Marc Anthony and Octavius marking names on a list for murder. The scenes are next to each other (though parallel episodes don't have to be), but thematically there is clearly a comparison to be made.
One quick proviso: "parallel episodes" might simply mean two parts of a text that - although written one after the other, or at different points in a text - are supposed chronologically to happen at the same time. This is a less usual use of the term, though.
Hi, This is a great question! Think about a story in which there are two girls and two boys, and during the story, both couples get into big arguments. The arguments might not be about the same things, but the scenes in the story have in common that each has a couple in an argument. Another example might be two characters who are struggling to fit in at school. There could be episodes showing each of their struggles. These characters might have different reasons for not fitting in easily, but there are parallels, meaning similarities, between their struggles. When episodes have some important things in common, we call them parallel episodes. Think for a moment what it means to have parallel roads. They are not the same, but they are in running the same direction. So, scenes or episodes in a novel that have similarities in character, action, or outcome can be said to be parallel. Good luck in your studies!